The period and Q of the Chandler wobble of Mars

The calculations of the Chandler wobble period TW have been performed for a set of interior structure models of Mars with 50- and 100-km thick crust and averaged crustal density varying in the range 2700-3200 kg/m3. The models satisfy new values for the moment of inertia and the elastic tidal Love number k2s. The observational data constrain the radius of a liquid core to be within 1700-1800 km. Because of inelasticity the value of TW depends on frequency (as the Love number depends on frequency). We assume that the power creep function is valid for description of inelastic processes in Martian interiors in the range of periods from T2Ph=5.55 h to TW≈200 days. Then the dynamical shear modulus μ0(σ) and dissipative factor Qμ(σ) varies with frequency σ as σn. As a reference frequency we used the frequency of Phobos' tidal wave σt. The substitution of k(σt) in the formula for TW gives the estimate for the minimum model value of the Chandler period 202.8⩽TWt⩽203.4 days. For the exponent of creep function 0.1⩽n⩽0.2 (by analogy with the calculations for the Earth) the shift of the Chandler period to longer periods due to inelasticity δTW is in the interval 0.981⩽δTW⩽1.42 days. Combining both estimates we obtain the interval for the model value of Chandler wobble period of Mars as 203.8⩽TWt+δTW⩽204.8